Chapter 15 Correlation Flashcards
What is the Pearson Correlation?
The Pearson correlation measures the degree and the direction of the linear relation between two variables
How is the Pearson Correlation identified?
By the letter r
The Pearson correlation is identified by the letter r, how is the correlation conceptually calculated? i.e. the degree of what divided by what?
the degree to which x and y vary together divided by the degree to which x and y vary separately
OR written as
the covariability of x and y divided by the variability of x and y separately
What does the Sum of Squares (SS) measure?
the variability for a single variable
What does the sum of products (SP) measure?
the co-variability between two variables
What is the difference between the way the SS and the SP are calculated?
The SS uses squared values and the SP uses products
What is the deviation?
The distance from the mean
What is the standard deviation?
The standard deviation is the square root of the variance and provides a measure of the standard distance from the mean.
What is the variance?
The mean of the squared deviations. Variance is the average squared distance from the mean
Why wont the average of the deviation scores work as representing the variability?
Because the average of the deviation scores equal zero, due to the positive and negative scores cancelling each other out.
How is the variance defined?
Variance is the mean squared deviation which equals the sum of squared deviations divided by the number of scores
What does the Pearson Correlation consist of?
The ratio comparing the covariability of X and Y to the variability of X and Y separately
Where and why are the pearson correlation used?
a. For prediction
b. for validity
c. for reliability
d. theory verification
What is the reliability of a measurement tied to?
The notion that each individual measurement includes an element of error. This is expressed as an equation
measured score = true score + error
How can correlation help researchers to measure reliability?
By taking two measurements for each individual, it is possible to compute the correlation between the first score and second score. A strong positive correlation indicates a good level of reliability. A weak correlation indicates that there is not a consistent relationship between the first score and the second score; that is, a weak correlation indicates poor reliability.
What are four rules when interpreting correlations?
- correlation simply describes a relationship between two variables, it does not explain why the two variables are related.
- the value of the correlation can be affected greatly by the range of scores represented in the data
- one or two extreme data points, often called outliers, can have a dramatic effect on the value of a correlation
- To describe how accurately one variable predicts the other, you must square the correlation. thus, a correlation of r=0.5 means that one variable partially predicts the other, but the predictable portion is only r2=.5 squared= .25 (25% of the total variability)
What is the coefficient of determination
r2 (the pearson coefficient squared)
what does the coefficient of determination measure?
the proportion of variability in one variable that can be determined from the relationship with the other variable.
